Spherically Symmetric Gravitational Collapse

Abstract

In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop this formalism. The formulae for extrinsic curvature tensor are obtained. The general form of the surface energy-momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained show the regions for the collapse and expansion of the shell.

12 pages, 4 figures, accepted for publication in Mod. Phys. Lett. A

References in corpus (13)

• Dynamics of dissipative gravitational collapse
• Gravitational Collapse with a Cosmological Constant
• Gravitational collapse to toroidal, cylindrical and planar black holes
• Black Hole Formation from Collapsing Dust Fluid in a Background of Dark Energy
• Gravitational Collapse of Dust with a Cosmological Constant
• Gravitational Perfect Fluid Collapse With Cosmological Constant
• Gravitational Collapse of Cylindrical Shells Made of Counter-Rotating Dust Particles
• Cylindrical Collapse and Gravitational Waves
• Quasi-spherical collapse with cosmological constant
• Non-adiabatic collapse of a quasi-spherical radiating star
• Gravitational Collapse of Perfect Fluid
• Plane Symmetric Gravitational Collapse
• Gravitational dust collapse with cosmological constant

Cited by in corpus (12)

• Effects of Electromagnetic Field on Gravitational Collapse
• Dynamics of Charged Plane Symmetric Gravitational Collapse
• Charged Perfect Fluid Cylindrical Gravitational Collapse
• Dynamics of Scalar Thin-Shell for a Class of Regular Black Holes
• Radiating Gravitational Collapse with an Initial Inhomogeneous Energy Density Distribution
• Gravitational Collapse: Expanding and Collapsing Regions
• Gravitational Charged Perfect Fluid Collapse in Friedmann Universe Models
• Radiating Gravitational Collapse with Shearing Motion and Bulk Viscosity Revisited
• Expanding and Collapsing Scalar Field Thin Shell
• Non-Commutative Correction to Thin Shell Collapse in Reissner Nordstr$\ddot{o}$m Geometry
• Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
• Dynamical model of expansion free dissipative perfect fluids in general relativity